Results 251 to 260 of about 165,990,627 (290)

Substructural Logic of Proofs

2013
In this paper, we introduce substructural variants of Artemov's logic of proofs. We show a few things here. First, we introduce a bimodal logic that has both the exponential operator in linear logic and an S4 modal operator which does not bring in any structural feature.
Hidenori Kurokawa, Hirohiko Kushida
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The basic logic of proofs

1993
Propositional Provability Logic was axiomatized in [5]. This logic describes the behaviour of the arithmetical operator “y is provable”. The aim of the current paper is to provide propositional axiomatizations of the predicate “x is a proof of y”by means of modal logic, with the intention of meeting some of the needs of computer science.
Sergei N. Artëmov, Tyko Straßen
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Proof Theories for Semilattice Logics

Mathematical Logic Quarterly, 1987
This paper presents original results which unify much of the research on the semilattice relevant logics \({}^ uT_ +\), \({}^ uR_ +\), \({}^ uTW_ +\), \({}^ uRW_ +\) introduced by \textit{A. Urquhart} [The semantics of entailment (University of Pittsburgh Doctoral Dissertation) (1973); J. Symb.
Steve Giambrone, Alasdair Urquhart
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Models for the logic of proofs

1997
The operational logic of proofs \(\mathcal{L}\mathcal{P}\)was introduced by S. Artemov [1] as an operational version of 54. In this paper, we define a model for \(\mathcal{L}\mathcal{P}\)and prove the corresponding completeness theorem. Using this model, we prove the decidability of a variant of \(\mathcal{L}\mathcal{P}\)axiomatized by a finite set of ...
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The Logic of Geometric Proof

2006
Logical studies of diagrammatic reasoning—indeed, mathematical reasoning in general—are typically oriented towards proof-theory. The underlying idea is that a reasoning agent computes diagrammatic objects during the execution of a reasoning task. These diagrammatic objects, in turn, are assumed to be very much like sentences.
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Proof Analysis in Modal Logic

Journal of Philosophical Logic, 2005
Labelled sequent calculi, which internalize Kripke semantics into inference systems, are introduced for many normal modal logics such as K, T, K4, KB, S4, TB, S5 and GL. The calculi are cut-free and contraction-free and the validity of structural properties, invertibility of rules, admissibility of substitution, contraction and cut are proved ...
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Proof Nets for Classical Logic

Journal of Logic and Computation, 2003
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Completeness Proofs for Diagrammatic Logics

2012
We identify commonality in the completeness proof strategies for Euler-based logics and show how, as expressiveness increases, the strategy readily extends. We identify a fragment of concept diagrams, an expressive Euler-based notation, and demonstrate that the completeness proof strategy does not extend to this fragment.
Jim Burton 0001, Gem Stapleton, John Howse   +2 more
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Logic Programming with Focusing Proofs in Linear Logic

Journal of Logic and Computation, 1992
Summary: The deep symmetry of linear logic makes it suitable for providing abstract models of computation, free from implementation details which are, by nature, oriented and nonsymmetrical. I propose here one such model, in the area of logic programming, where the basic computational principle is: \[ \text{Computation}=\text{Proof search}.
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Logic and proofs

2018
We formulate mathematical arguments in our natural language. But our everyday language is often ambiguous, and quite often you hear logical fallacies. Therefore, if you want to argue reliably then you should know well both the basic logical structures and the phrases we use to express them.
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